Illuminating Massive Black Holes With White Dwarfs: Orbital Dynamics and High Energy Transients from Tidal Interactions

White dwarfs (WDs) can be tidally disrupted only by massive black holes (MBHs) with masses less than $\sim10^5 M_\odot$. These tidal interactions feed material to the MBH well above its Eddington limit, with the potential to launch a relativistic jet. The corresponding beamed emission is a promising signpost to an otherwise quiescent MBH of relatively low mass. We show that the mass transfer history, and thus the lightcurve, are quite different when the disruptive orbit is parabolic, eccentric, or circular. The mass lost each orbit exponentiates in the eccentric-orbit case leading to the destruction of the WD after several tens of orbits. We examine the stellar dynamics of clusters surrounding MBHs to show that single-passage WD disruptions are substantially more common than repeating encounters. The $10^{49}$ erg s$^{-1}$ peak luminosity of these events makes them visible to cosmological distances. They may be detectible at rates of as many as tens per year by instruments like Swift. In fact, WD-disruption transients significantly outshine their main-sequence star counterparts, and are the most likely tidal interaction to be detected arising from MBHs with masses less than $10^5 M_\odot$. The detection or non-detection of such WD-disruption transients by Swift is, therefore, a powerful tool to constrain lower end of the MBH mass function. The emerging class of ultra-long gamma ray bursts all have peak luminosities and durations reminiscent of WD disruptions, offering a hint that WD-disruption transients may already be present in existing datasets.